Jorge received a 3.1% increase in his pay at work. If he now makes $8.00 per hour, how much was he making before his raise? (Rou
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The x-intercept is the point at which the function intersects the x-axis.
For any point on the x-axis, y = 0. Thus we can plug in 0 for y and solve for x.
Let's split the middle on this quadratic.
To do this we need to find two numbers that add to equal -6 and multiply to equal -72. (-3 times 24)
Consider ways to multiply to get 72.
72 = 36 ×2...that's not going to work.
72 = 24 × 3
72 = 18 × 4
72 = 12 × 6...and 12 minus 6 is 6!
Let's add our signs; our numbers are -12 and 6.
Now, split the middle and factor.
Now you should know that anything multiplied by zero is zero.
So any value that makes one of those factors equal zero is an x-intercept.
Solve each of these equations.
-3x+6 = 0
-3x = -6
x = 2
x+4 = 0
x = -4
Oh, and since all parabolas (graphs of quadratics) are symmetrical, our axis of symmetry will be the average between the two, which is x=-1.
Now for our y-intercepts. For any points on the y-axis, x=0, so if we plug in 0 for x and solve for y we'll get our y-intercept.
y = -3×0² - 6×0 + 24
y = 0 - 0 + 24
y = 24
What about our vertex? Well, we know it's going to line up with the axis of symmetry, so let's just plug in -1 for x.
y = -3×-1² - 6×-1 + 24
y = -3×1 -6×-1 + 24
y = -3 + 6 + 24
y = 27
Thus the vertex is (-1, 27)
The y value is not going to exceed 27, as this is a decreasing quadratic, (we already know y=24 is a possibilty) and this equation goes downwards infinitely, so our range is (-∞, 27)
As for x, well, it's sort of the input for our equation, meaning it can be whatever we want it to be. Thus the domain is (-∞, ∞)
For any point on the x-axis, y = 0. Thus we can plug in 0 for y and solve for x.
Let's split the middle on this quadratic.
To do this we need to find two numbers that add to equal -6 and multiply to equal -72. (-3 times 24)
Consider ways to multiply to get 72.
72 = 36 ×2...that's not going to work.
72 = 24 × 3
72 = 18 × 4
72 = 12 × 6...and 12 minus 6 is 6!
Let's add our signs; our numbers are -12 and 6.
Now, split the middle and factor.
Now you should know that anything multiplied by zero is zero.
So any value that makes one of those factors equal zero is an x-intercept.
Solve each of these equations.
-3x+6 = 0
-3x = -6
x = 2
x+4 = 0
x = -4
Oh, and since all parabolas (graphs of quadratics) are symmetrical, our axis of symmetry will be the average between the two, which is x=-1.
Now for our y-intercepts. For any points on the y-axis, x=0, so if we plug in 0 for x and solve for y we'll get our y-intercept.
y = -3×0² - 6×0 + 24
y = 0 - 0 + 24
y = 24
What about our vertex? Well, we know it's going to line up with the axis of symmetry, so let's just plug in -1 for x.
y = -3×-1² - 6×-1 + 24
y = -3×1 -6×-1 + 24
y = -3 + 6 + 24
y = 27
Thus the vertex is (-1, 27)
The y value is not going to exceed 27, as this is a decreasing quadratic, (we already know y=24 is a possibilty) and this equation goes downwards infinitely, so our range is (-∞, 27)
As for x, well, it's sort of the input for our equation, meaning it can be whatever we want it to be. Thus the domain is (-∞, ∞)
Answer:
If we compare the p value and the significance level assumed we see that
so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its NOT significant higher than 0.3 at 1% of signficance.
Step-by-step explanation:
Data given and notation
represent the sample mean
represent the sample standard deviation for the sample
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is higher than 3, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is > 30 and we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:
(1)
z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
Since is a one side test the p value would be:
Conclusion
If we compare the p value and the significance level assumed we see that
so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its NOT significant higher than 0.3 at 1% of signficance.